A SpatioTemporal Model for Seasonal Influenza

Abstract

This paper describes an attempt to model seasonal influenza using the SpatioTemporal Epidemiological Modeler (STEM). Ten years of influenza data collected at 49 locations in Israel by the Israeli Center for Disease Control was used to fit the model, and a deterministic SIR(S) compartmental disease model was extended to account for seasonal variation in transmission rates as well as mixing of infected individuals between geographic regions. An adaptive step-size ordinary differential equation solver generated the time series data, and model parameters were fitted to the first few seasonal cycles of the experimental data and compared to subsequent cycles. The model used a sinusoidal seasonal variation of the transmission rate using an exponent parameter, and the best fit exponent was found to be very close to the square root of a sine function (exponent = 0.55), rather than the simple sine function typically used. Other results found that the transmission coefficient was high most of the year and that spatial mixing was high with 90% of people regularly visiting adjacent regions. The study obtained an excellent fit for the first two annual cycles (with less than 3% Root Mean Square error), with rapidly degrading accuracy in subsequent years. Finally, the annual variation in influenza species and strain suggests that a multi-serotype model for seasonal flu should provide better predictive capability. STEM and the mathematical models used in the study are all open source, available at www.eclipse.org/stem. An extension of the model to incorporate multiple serotypes will be studied in the future.